By A. Auge, G. Lube, D. Weiß (auth.), Wolfgang Hackbusch, Gabriel Wittum (eds.)
Galerkin/Least-Squares-FEM and Anisotropic Mesh Refinement.- Adaptive Multigrid tools: The UG Concept.- Finite quantity tools with neighborhood Mesh Alignment in 2-D.- a brand new set of rules for Multi-Dimensional Adaptive Numerical Quadrature.- Adaptive answer of One-Dimensional Scalar Conservation legislation with Convex Flux.- Adaptive, Block-Structured Multigrid on neighborhood reminiscence Machines.- Biorthogonal Wavelets and Multigrid.- Adaptive Multilevel-Methods for main issue difficulties in 3 area Dimensions.- Adaptive aspect Block Methods.- Adaptive Computation of Compressible Fluid Flow.- On Numerical Experiments with vital distinction Operators on exact Piecewise Uniform Meshes for issues of Boundary Layers.- The field process for Elliptic Interface difficulties on in the neighborhood sophisticated Meshes.- Parallel regular Euler Calculations utilizing Multigrid equipment and Adaptive abnormal Meshes.- An Object-Oriented strategy for Parallel Self Adaptive Mesh Refiement on Block dependent Grids.- A Posteriori errors Estimates for the Cell-Vertex Finite quantity Method.- Mesh version through a Predictor-Corrector-Strategy within the Streamline Diffusion approach for Nonstationary Hyperbolic Systems.- at the V-Cycle of the totally Adaptive Multigrid Method.- Wavelets and Frequency Decomposition Multilevel equipment.
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Additional info for Adaptive Methods — Algorithms, Theory and Applications: Proceedings of the Ninth GAMM-Seminar Kiel, January 22–24, 1993
3 Drift Chamber This problem solves the Laplacian -L'lu = 0 in the domain given by Fig. 5. The boundary conditions are of Dirichlet and Neumann type as indicated in the figure. The feature of this problem are the small wires with Dirichlet boundary conditions that must be resolved on the coarse grid. 005 mm, while the whole chamber is 4 mm wide and 1 mm thick. So one has to trade off between a coarse grid with 29 Table 4: Results for different solver/smoother combinations for the drift chamber problem.
Starting with a fine and structured grid, coarsening is performed only in those co-ordinate directions, in which the scale of the equation is already resolved. g. ). 3 Such a sequence of coarse grids yields a rob'ust m'ulti-grid method for the anisotropic model problem (9) without using a special smoother, since the coar'se grzd resolves the scale in the direction where the smoother does not work. This semi-coarsening approach, however, is based on the use of fine grids whIch do not resolve the differential scale, otherwise there would be no semi-coarsening.
41 ) (42) The exact stationary solution is given by a straight diagonal line which separates two constant states. The numerical results are shown in Figure 7 on a grid which is not aligned and on a grid which is aligned with the shock respectively. The resolution of the shock on the aligned grid is much better than for the other one. Therefore this example shows us, that it is necessary to align the triangles in an unstructured grid with the main structures of the solutions. 46 Figure 7 The second testproblem is to solve OtU + yOxu - xoyu = ° n:= [0,1] III x [0,1] (43) with initial values U(x,y,O) u(x, y, 0) ° if x = 0, y:::; ~ (44) (45) otherwise and the corresponding boundary conditions on the inflow part of the boundary U(x, y, t) u(x, y, t) if o x = 0, otherwise y :::; ~ (46) (47) 47 The exact stationary solution is given by a quarter of a circle which separates two constant states.
Adaptive Methods — Algorithms, Theory and Applications: Proceedings of the Ninth GAMM-Seminar Kiel, January 22–24, 1993 by A. Auge, G. Lube, D. Weiß (auth.), Wolfgang Hackbusch, Gabriel Wittum (eds.)